Tianyi Chu

Publications:

Contour dynamics is a computational technique to solve for the motion of vortices
in incompressible inviscid flow. It is a Lagrangian technique in which the motion of contours
is followed, and the velocity field moving the contours can be computed as integrals along
the contours. Its best-known examples are in two dimensions, for which the vorticity between
contours is taken to be constant and the vortices are vortex patches, and in axisymmetric
flow for which the vorticity varies linearly with distance from the axis of symmetry. This review
discusses generalizations that incorporate additional physics, in particular, buoyancy effects and
magnetic fields, that take specific forms inside the vortices and preserve the contour dynamics
structure. The extra physics can lead to time-dependent vortex sheets on the boundaries, whose
evolution must be computed as part of the problem. The non-Boussinesq case, in which density
differences can be important, leads to a coupled system for the evolution of both mean interfacial
velocity and vortex sheet strength. Helical geometry is also discussed, in which two quantities
are materially conserved and whose evolution governs the flow.